3.1 Inequalities and Their Graphs: Inequality: A mathematical sentence that uses and inequality...
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Transcript of 3.1 Inequalities and Their Graphs: Inequality: A mathematical sentence that uses and inequality...
3.1 Inequalities and Their Graphs:
Inequality: A mathematical sentence that uses and inequality symbol (< , >, ≤, ≥) to compare the values of two expressions.
Solution of an Inequality: Any number that makes the inequality true.
SYMBOLS OF INEQUALITY:( < ) Less than : Any number that is to the left not including the number itself.
x < -1
SYMBOLS OF INEQUALITY:
( > ) Greater than: Any number that is to the right not including the number itself.
x > 1
SYMBOLS OF INEQUALITY:
( ≤ ) Less than or equal to : Any number that is to the left including the number itself.
x ≤ 0
SYMBOLS OF INEQUALITY:
( ≥ ) Greater than or equal to : Any number that is to the right including the number itself.
x ≥ 2
WRITING INEQUALITIES: We can use the inequality symbols to write verbal expressions into math sentences and use the number line to represent the solution.
Ex:All real numbers greater than 3.
http://player.discoveryeducation.com/index.cfm?guidAssetId=A9FA7702-1F9F-4A4D-9E51-2FF98439A759
WRITING INEQUALITIES: (SOLUTION) All real numbers greater than 3.
Let x = real numbers
Greater than > x > 3
Graph:
REAL-WORLD:
Joseph saved last month a total of $115 dollars for doing house shores. He is planning to spend $30 on a video game and the he wants to buy music sheet booklets. If each booklet costs $15, create a graph to represent the number of booklets he can buy.
Solution: Joseph saved $115Buys video game - 30 Music sheet booklets $15x
To find how many he can buy: 15x + 30 ≤ 150
15x ≤ 120
x ≤ 8 booklets.
Subtract 30Divide by 15
YOU TRY IT:
Ex:What inequality represent the verbal
expression:
The subtraction of t and 7 is less than -3.
SOLUTION:The sum and t and 7 is less than -3.
t, 7, - 3subtraction -Less than <
t - 7 < -3
Graph: ( isolate t t < 4)
IDENTIFYING SOLUTIONS: We can use substitution to see if a given number is a solution to an equation.Ex: Identify solutions by evaluation:
13 – 7y ≤ 6
a) 1 b) -1, c) 3 d) -5
SOLUTION:
a) 1 13 – 7( 1) ≤ 613 – 7 ≤ 6 6 ≤ 6 TRUE
13 – 7y ≤ 6
a) -1 13 – 7( -1) ≤ 6 13 + 7 ≤ 6 20 ≤ 6 FALSE
13 – 7y ≤ 6Thus 1 is a solution.
Thus -1 is NOT a solution.
SOLUTION:
a) 3 13 – 7( 3) ≤ 613 – 21 ≤ 6
-7 ≤ 6 TRUE
13 – 7y ≤ 6
a) 5 13 – 7( 5 ) ≤ 613 - 35 ≤ 6
- 12 ≤ 6 TRUE
13 – 7y ≤ 6Thus 3 is a solution.
Thus 5 is a solution.
VIDEOS: Graphing Inequalities
https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/graphing-linear-inequalities/v/solving-and-graphing-linear-inequalities-in-two-variables-1
https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/graphing-linear-inequalities/v/graphing-inequalities